Theoretical Models for Drug Delivery to Solid Tumors

Abstract

A cancer drug's effectiveness is contingent upon on its ability to reach all parts of the tumor. The distribution of drug in the tumor depends on several transport processes and depends on the physicochemical properties of the drug. These factors can lead to highly heterogeneous distributions of drug in the tumor interstitial space, leaving parts of the tumor unreached, and make it difficult to predict cellular exposure and understand its dependence on key system parameters. Theoretical models are powerful tools that can provide insight by simulating conditions that cannot be achieved or observed experimentally. Here, a Green's function method is utilized to simulate three-dimensional time-dependent diffusion and uptake of drugs in solid tumors with realistic vascular geometry. Regimes dependent on the time scales for transport are used to determine whether spatial and temporal effects must be resolved to predict cellular exposure. Simulations are performed to show the relationship between the plasma pharmacokinetics and cellular exposure for these regimes. Steep gradients in concentration arise when time scales for diffusion and uptake are comparable, implying that models based on well mixed compartments are inaccurate. Effects of linear and nonlinear kinetics of drug uptake on cellular exposure are demonstrated. The drug doxorubicin is commonly used against solid tumors. Cellular exposure to doxorubicin is complicated in vivo by its transport and physicochemical properties. The Green's function method is used to describe the in vivo transport and kinetics of doxorubicin, using parameters derived from in vitro results. Simulations show agreement with observed in vivo distributions of doxorubicin in tumor tissue as well as in vitro kinetics, and provide a link between the two types of experimental observations. The method is applied to the class of cancer drugs called antibody-drug conjugates (ADCs) which consist of a humanized antibody conjugated to extremely toxic small molecular weight drugs. ADCs exhibit complex in vivo kinetics dependent on many design parameters. A phenomenon exhibited by ADCs is the bystander effect, i.e. non-targeted cell killing, which is difficult to analyze based on in vivo observations. Simulations results agree with the observed in vivo distribution of ADCs in tumor tissue and with experimentally observed bystander effects. In summary, the the models presented here provide a novel approach for simulating the complex transport and cellular uptake kinetics exhibited by several cancer drugs. The models give a mechanistic basis for predicting cellular exposure to drugs which can aid, explain, and direct experimental approaches for improving cancer treatment.